Agree. Not the OS, but any other software can be installed in an external hard drive. One thing must be know is every time you disconnect and connect the USB drive you take a risk. Windows can give you a different letter to your drive and this can ruin your life!!!
For example, if you have a pc with a C hard drive and D cdrom drive. You add an external hard drive. Windows assign the E letter.
If later you remove the E drive, insert an USB drive and later the USB hard drive, windows can provide the USB drive letter to your memory instead of your hard disk, and this can be a big problem.